Tag Archives: #paint50

Interactive Order Nine Magic Square Puzzle Art

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Painting number 17 of the 50 Paintings for 2012 goal, now available as a standard greeting card or museum-quality fine art print– rolled, under glass or on canvas.

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This interactive painting is a jumbled order-9 square, or a semimagic square, meaning the rows and columns add to the same number but the diagonals do not. Jumbling the magic square into a semimagic square actually makes it more challenging to solve as the pattern is more difficult. However, to make it a bit easier, only prime numbers have been omitted. Buy this piece on canvas and solve it with a paint writer or a paint pen to make it truly interactive. Difficulty level: Intermediate.

Recreational mathematics includes logic puzzles and other puzzles that require deductive reasoning, the aesthetics of mathematics, and peculiar or amusing stories and coincidences about mathematics and mathematicians. Some of the more well-known topics in recreational mathematics are magic squares and fractals. Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study of mathematics.

In recreational mathematics, a magic square of order n is an arrangement of n-squared numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n-squared. The term “magic square” is also sometimes used to refer to any of various types of word square.

Magic squares have fascinated humanity throughout the ages, and have been around for over 4,120 years. They are found in a number of cultures, including Egypt and India, engraved on stone or metal and worn as talismans, the belief being that magic squares had astrological and divinatory qualities, their usage ensuring longevity and prevention of diseases.

Magic squares were known to Chinese mathematicians, as early as 650 BCE and Arab mathematicians, possibly as early as the 7th century, when the Arabs conquered northwestern parts of the Indian subcontinent and learned Indian mathematics and astronomy, including other aspects of combinatorial mathematics. The first magic squares of order 5 and 6 appear in an encyclopedia from Baghdad circa 983 CE, the Encyclopedia of the Brethren of Purity (Rasa’il Ihkwan al-Safa); simpler magic squares were known to several earlier Arab mathematicians. Some of these squares were later used in conjunction with magic letters as in (Shams Al-ma’arif) to assist Arab illusionists and magicians.

Chinese literature dating from as early as 650 BC tells the legend of Lo Shu or “scroll of the river Lo”. In ancient China there was a huge flood. The great king Yu tried to channel the water out to sea where then emerged from the water a turtle with a curious figure/pattern on its shell; circular dots of numbers which were arranged in a three by three grid pattern such that the sum of the numbers in each row, column and diagonal was the same: 15, which is also the number of days in each of the 24 cycles of the Chinese solar year. This pattern, in a certain way, was used by the people in controlling the river.

The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three in which 1 is at the bottom and 2 is in the upper right corner. Every normal magic square of order three is obtained from the Lo Shu by rotation or reflection.

The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos.

The order-4 magic square in Albrecht Dürer’s engraving Melencolia I is believed to be the first seen in European art. It is very similar to Yang Hui’s square, which was created in China about 250 years before Dürer’s time. The sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, and the corner squares(of the 4×4 as well as the four contained 3×3 grids).

(Visit Wikipedia for the complete original article on Magic Square.)

Red Wine Painting

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Painting number 16 of the 50 Paintings for 2012 goal, now available as a standard greeting card or museum-quality fine art print– rolled, under glass or on canvas.

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Wine is an alcoholic beverage, made of fermented fruit juice, usually from grapes. The natural chemical balance of grapes lets them ferment without the addition of sugars, acids, enzymes, or other nutrients. Grape wine is produced by fermenting crushed grapes using various types of yeast. Yeast consumes the sugars in the grapes and converts them into alcohol. Different varieties of grapes and strains of yeasts produce different types of wine.

Wines made from other fruits, such as apples and berries, are usually named after the fruit from which they are produced (for example, apple wine or elderberry wine) and are generically called fruit wine or country wine (not to be confused with the French term vin de pays). Others, such as barley wine and rice wine (i.e., sake), are made from starch-based materials and resemble beer and spirit more than wine, while ginger wine is fortified with brandy. In these cases, the term “wine” refers to the higher alcohol content rather than the production process.

The commercial use of the English word “wine” (and its equivalent in other languages) is protected by law in many jurisdictions. Wine has a rich history dating back thousands of years, with the earliest known production occurring around 8,000 years ago on the territory of modern-day Georgia. It first appeared in the Balkans at about 4500 BC and was very common in ancient Greece, Thrace and Rome. Wine has also played an important role in religion throughout history. The Greek god Dionysus and the Roman equivalent Bacchus represented wine, and the drink is also used in Christian Eucharist ceremonies and the Jewish Kiddush (among many other Jewish ceremonies).

(Visit Wikipedia for the complete original article on Wine.)

Champagne Painting

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Painting number 15 of the 50 Paintings for 2012 goal, now available as a standard greeting card or museum-quality fine art print– rolled, under glass or on canvas.

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Sparkling wine is a wine with significant levels of carbon dioxide in it making it fizzy. The carbon dioxide may result from natural fermentation, either in a bottle, in a large tank designed to withstand the pressures involved, or as a result of carbon dioxide injection.

The classic example of a sparkling wine is Champagne, but this wine is exclusively produced in the Champagne region of France. Many sparkling wines are produced in other countries and regions, such as Espumante in Portugal, Cava in Spain, Franciacorta, Trento, Oltrepo Pavese Metodo Classico and Asti in Italy (the generic Italian term for sparkling wine being spumante) and Cap Classique in South Africa. Most countries reserve the word Champagne for a specific type from the Champagne region of France. The French terms “Mousseux” or “Cremant” are used to refer to sparkling wine not made in the Champagne region. German and Austrian sparkling wines are called Sekt. The United States is a significant producer of sparkling wine with producers in numerous states. Recently the United Kingdom, which produced some of the earliest examples of sparkling wine, has started producing sparkling wines again.

The Romans were the first to plant vineyards in this area of northeast France with the region being cultivated by at least the 5th century, possibly earlier. Wines from the Champagne region were known before medieval times. Churches owned vineyards and monks produced wine for use in the sacrament of Eucharist. French kings were traditionally anointed in Reims and Champagne wine was served as part of coronation festivities. The Champenois were envious of the reputation of the wines made by their Burgundian neighbours to the south and sought to produce wines of equal acclaim. However, the northerly climate of the region gave the Champenois a unique set of challenges in making red wine. At the far extremes of sustainable viticulture, the grapes would struggle to ripen fully and often would have bracing levels of acidity and low sugar levels. The wines would be lighter bodied and thinner than the Burgundy wines they were seeking to outdo.

Contrary to legend and popular belief, Dom Perignon did not invent sparkling wine. The oldest recorded sparkling wine is Blanquette de Limoux, which was apparently invented by Benedictine Monks in the Abbey of Saint Hilaire near Carcassonne in 1531. Over a century later, the English scientist and physician Christopher Merret documented the addition of sugar to a finished wine to create a second fermentation six years before Dom Perignon set foot in the Abbey of Hautvillers and almost 40 years before it was claimed that the famed Benedictine monk invented Champagne. Merret presented the Royal Society with a paper in which he detailed what is now called méthode champenoise in 1662.

Although Dom Perignon did not invent Champagne, he did develop many advances in production of the drink, including holding the cork in place with a wire collar (muselet) to withstand the fermentation pressure. In France, the first sparkling Champagne was created accidentally; its pressure led it to be called “the devil’s wine” (le vin du diable) as bottles exploded or the cork jolted away.

Champagne first gained world renown because of its association with the anointment of French kings. Royalty from throughout Europe spread the message of the unique sparkling wine from Champagne and its association with luxury and power in the 17th, 18th and 19th century. The leading manufacturers devoted considerable energy to creating a history and identity for their wine, associating it and themselves with nobility and royalty. Through advertising and packaging they sought to associate Champagne with high luxury, festivities, and rites of passage. Their efforts coincided with the emergence of a middle class that was looking for ways to spend its money on symbols of upward mobility.

(Visit Wikipedia for the complete original article on Champagne.)

Vanilla Molecule Painting

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Painting number 14 of the 50 Paintings for 2012 goal, now available as a standard greeting card or museum-quality fine art print– rolled, under glass or on canvas.

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Vanilla is a flavoring derived from orchids of the genus Vanilla, primarily from the Mexican species, Flat-leaved Vanilla (V. planifolia). The word vanilla derives from the Spanish word “vainilla”, little pod. Pre-Columbian Mesoamerican peoples cultivated vanilla and Spanish conquistador Hernan Cortes is credited with introducing both vanilla and chocolate to Europe in the 1520s.

Vanilla is the second most expensive spice after saffron, because growing the vanilla seed pods is labor-intensive. Despite the expense, vanilla is highly valued for its flavor, which author Frederic Rosengarten, Jr. described in The Book of Spices as “pure, spicy, and delicate” and its complex floral aroma depicted as a “peculiar bouquet”. As a result, vanilla is widely used in both commercial and domestic baking, perfume manufacture and aromatherapy.

There are three main commercial preparations of natural vanilla: whole pod, powder and extract.

Vanilla flavoring in food may be achieved by adding vanilla extract or by cooking vanilla pods in the liquid preparation. A stronger aroma may be attained if the pods are split in two, exposing more of a pod’s surface area to the liquid. In this case, the pods’ seeds are mixed into the preparation. Natural vanilla gives a brown or yellow color to preparations, depending on the concentration. Good-quality vanilla has a strong aromatic flavor, but food with small amounts of low-quality vanilla or artificial vanilla-like flavorings are far more common, since true vanilla is much more expensive.

A major use of vanilla is in flavoring ice cream. The most common flavor of ice cream is vanilla, and thus most people consider it to be the “default” flavor. By analogy, the term “vanilla” is sometimes used as a synonym for “plain”. Although vanilla is a prized flavoring agent on its own, it is also used to enhance the flavor of other substances, to which its own flavor is often complementary, such as chocolate, custard, caramel, coffee, cakes, and others.

The ice cream and chocolate industries together comprise 75% of the market for vanillin as a flavoring, with smaller amounts being used in confections and baked goods.

The cosmetics industry also uses vanilla to make perfume.

Though there are many compounds present in the extracts of vanilla, the compound vanillin featured in this painting is primarily responsible for the characteristic flavor and smell of vanilla.

(Visit Wikipedia for the complete original article on Vanilla.)

Hot Chili Pepper Molecule Painting

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Painting number 12 of the 50 Paintings for 2012 goal, now available as a standard greeting card or museum-quality fine art print– rolled, under glass or on canvas.

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Chili pepper (also chile pepper or chilli pepper, from Nahuatl chilli) is the fruit of plants from the genus Capsicum, members of the nightshade family, Solanaceae. The term in British English and in Australia, New Zealand, India, Malaysia and other Asian countries is just chilli without pepper.

Chili peppers originated in the Americas. After the Columbian Exchange, many cultivars of chili pepper spread across the world, used in both food and medicine. Chili peppers have been a part of the human diet in the Americas since at least 7500 BC. There is archaeological evidence at sites located in southwestern Ecuador that chili peppers were domesticated more than 6000 years ago, and is one of the first cultivated crops in the Central and South Americas that is self-pollinating.

Christopher Columbus was one of the first Europeans to encounter them (in the Caribbean), and called them “peppers” because they, like black and white pepper of the Piper genus known in Europe, have a spicy hot taste unlike other foodstuffs. Upon their introduction into Europe chilis were grown as botanical curiosities in the gardens of Spanish and Portuguese monasteries. But the monks experimented with the chilis’ culinary potential and discovered that their pungency offered a substitute for black peppercorns, which at the time were so costly that they were used as legal currency in some countries.

The substances that give chili peppers their intensity when ingested or applied topically are capsaicin (8-methyl-N-vanillyl-6-nonenamide) and several related chemicals, collectively called capsaicinoids. This painting represents a capsaicin molecule.

When consumed, capsaicinoids bind with pain receptors in the mouth and throat that are responsible for sensing heat. Once activated by the capsaicinoids, these receptors send a message to the brain that the person has consumed something hot. The brain responds to the burning sensation by raising the heart rate, increasing perspiration and release of endorphins.

The “heat” of chili peppers was historically measured in Scoville heat units (SHU), which is a measure of how much a chili extract must be diluted in sugar syrup before its heat becomes undetectable to a panel of tasters. Bell peppers rank at 0 SHU, New Mexico green chilis at about 1,500 SHU, jalapeños at 2,500–5,000 SHU, and habaneros at 300,000 SHU. The modern commonplace method for quantitative analysis of SHU rating uses high-performance liquid chromatography to directly measure the capsaicinoid content of a chili pepper variety. Pure capsaicin is a hydrophobic, colorless, odorless, and crystalline-to-waxy solid at room temperature, and measures 16,000,000 SHU.

Psychologist Paul Rozin suggests that eating chilis is an example of a “constrained risk” like riding a roller coaster, in which extreme sensations like pain and fear can be enjoyed because individuals know that these sensations are not actually harmful. This method lets people experience extreme feelings without any risk of bodily harm.

Eating chili is viewed as a warrior’s ritual in Japan because of its spicyness that gives individual fear and mental block. By forcing themselves to eat chili, warriors’ mental state gets stronger and may even feel invincible when stepping onto the battlefield. Eating chili has been a popular practice among the karate athletes who use it to strengthen their minds and determination.

(Visit Wikipedia for the complete original article on Chili Pepper.)